After earning a chemical engineering degree at the Eidgenössische Technische Hochschule (ETH, Federal Institute of Technology), in Zürich, Kuhn received a doctorate (1923) in physical chemistry from the University of Zürich for research on the photochemical decomposition of ammonia. As a Rockefeller Foundation fellow, he studied quantum mechanics at Niels Bohr’s Institute for Theoretical Physics in Copenhagen. Kuhn qualified as a lecturer (1927–28) at the University of Zürich and then moved to Germany to work with the German chemist Karl Freudenberg at the University of Heidelberg, where he produced a model interpretation of natural optical activity, which, along with the study of macromolecules, became one of his main research interests. As an associate professor at the Karlsruhe Technical University (1930–36), he worked with the German physical chemist Georg Bredig on the optical configuration of optically active compounds. He was appointed professor of physical chemistry at the University of Kiel (1936–39) and then returned to Switzerland as director of the Physico-Chemical Institute of the University of Basel (1939–63), where he also served as rector (1955–56).

In 1930, in what was probably the first application of statistical theory to polymerscience, Kuhn calculated the distribution of molecular weights of degraded cellulose by assuming that the molecule is broken up randomly. In 1933, while investigating polymer solution viscosity according to the theory of German chemist Hermann Staudinger, he used statistics to propose that macromolecular chains in solution are coiled rather than rigid, in contradiction of Staudinger’s view. Kuhn’s concept of “excluded volume” had important consequences for the theory of the hydrodynamic properties of polymer solutions, developed in 1949 by the American physical chemist Paul J. Flory. In 1945, in the first use of statistical mechanics to explain polymer properties, Kuhn applied his statistical model to the elasticity of rubber, which he later used to study muscle tissue and contraction. Outside of polymer science, Kuhn predicted the Mössbauer effect in 1929, 29 years before its discovery by German physicist Rudolf Mössbauer; achieved the first photochemical separation of isotopes (chlorine-35 and -37); developed a new type of countercurrent distillation column to obtain heavy water; explained the mechanism of urea concentration in the kidney; and explained the production of high gas pressure in fishes’ air bladders.